2011 IEEE/RSJ International Conference on Intelligent Robots and Systems September 25-30, 2011. San Francisco, CA, USA A Friction Differential and Cable Transmission Design for a 3-DOF Haptic Device with Spherical Kinematics Reuben Brewer, Adam Leeper, and J. Kenneth Salisbury Abstract— We present a new mechanical design for a 3-DOF haptic device with spherical kinematics (pitch, yaw, and pris- matic radial). All motors are grounded in the base to decrease inertia and increase compactness near the user’s hand. An aluminum-aluminum friction differential allows for actuation of pitch and yaw with mechanical robustness while allowing a cable transmission to route through its center. This novel cabling system provides simple, compact, and high-performance actuation of the radial DOF independent of motions in pitch and yaw. We show that the device’s capabilities are suitable for general haptic rendering, as well as specialized applications of spherical kinematics such as laparoscopic surgery simulation. I. INTRODUCTION As the application of haptics becomes more common and widespread, a need arises for haptic device designs which exhibit a slim form factor, are suitable over a range of scales, are mechanically robust, and are capable of general haptic Fig. 1: Our 3-DOF spherical haptic device. rendering as opposed to specialized applications. Spherical kinematics can be used to achieve such slim, scalable designs by concentrating the motors and transmission in the base of capabilities of our device make it suitable for general haptic- the device and leaving a slender, single-link connection to the rendering, and the novel mechanical design improves on user’s hand. Ideally, the base of the spherical haptic device existing designs for specific applications of spherical kine- can be stowed outside of the user’s view, and the single link matics, such as laparoscopic surgery simulation. that connects to the user’s hand can be easily stowed, unlike In the following sections, we begin with a discussion of re- a non-spherical device that connects to the user’s hand via lated work. We then describe the mechanical design, includ- several links. While there are many different haptic devices ing considerations for the friction differential, the prismatic with spherical kinematics, much remains to be desired in radial DOF, and the wrist gimbal. We anaylze characteristics terms of the simplicity, compactness, and robustness of their and capabilities of the device, including workspace, reso- mechanical design. Further, the usage of spherical kinematics lution, foward kinematics, jacobian, gravity compensation, has generally been limited to haptic devices aimed at specific maximum force, friction, dynamic range, and effective mass. applications, such as gaming and laparoscopic simulation, We conclude with a discussion of future work. rather than general haptic rendering. In this paper, we present a new mechanical design for a II. RELATED WORK spherical haptic device with pitch, yaw, and radial degree- The term “spherical kinematics” actually covers several of-freedom (DOF). Our design has a compact base and distinct kinematic combinations of pitch, yaw, roll, and a slim form factor that can be scaled to large devices and prismatic, radial DOF. The simplest of such devices, such as small devices. We achieve low inertia and high compact- [1] and the Impulse Engine 2000 (Immersion Corporation, ness/scalability through use of grounded motors and the San Jose, CA), are essentially 2-DOF, force-feedback joy- novel combination of a friction differential with a new way sticks that apply torques about pitch and yaw while keeping of routing a cable transmission through the differential to the user’s hand on the surface of a fixed sphere. The SHaDe a prismatic DOF. The simplicity of our design makes the haptic device [2] has 3 DOF that apply torques in roll, device easy to manufacture, assemble, and maintain, provid- pitch, and yaw centered about the user’s hand. Neither of ing reliable operation. The workspace and force-rendering these kinematic configurations allows for translation and R. Brewer and A. Leeper are with the Department of Mechani- force-rendering in arbitrary 3D space, making these devices cal Engineering, Stanford University, Stanford, CA, USA rdbrewer, unsuitable for the type of general haptic rendering possible [email protected] with devices like the Phantom [3] or Delta [4]. The addition J.K. Salisbury is with the Departments of Computer Science and Surgery, Stanford University, Stanford, CA, USA of a prismatic, radial DOF is critical to this general usability. [email protected] Two spherical devices that incorporate a radial DOF have 978-1-61284-455-8/11/$26.00 ©2011 IEEE 2570 Fig. 2: The motion variables are pitch φ (rotation about Y0), Fig. 3: The device workspace is a segment of a spherical yaw γ (rotation about X1), and radial ρ (translation shell. Pitch is on the range φ 2 [−50◦; +30◦], yaw is along Z2). on the range γ 2 [−25◦; +25◦], and extension is on the range ρ 2 [0; 86:5]mm. The radius of the inner surface of the workspace is 195:5mm been developed for general haptic interaction. In [5], the radial DOF was driven by a motor that that was attached to the moving pitch/yaw gimbal mechanism and converted losses [6], or via a very complex cable transmission [8]. rotary to linear motion via a cable. In [6], the radial DOF By grounding all motors, we have improved the inertial was driven by a cable that was routed in a flexible sleeve properties and compactness/form-factor. Our novel combi- from a grounded motor. However, the friction between the nation of an aluminum-aluminum friction differential and a sleeve and cable averaged 9N, uncompensated, and required new cable-routing technique produces a simpler, more robust active compensation based on force measurements to reduce transmission. We envision that our device could be a viable the friction to a little under 1N. competitor to commercially-available devices for general A spherical haptic device with a radial DOF is ideally- haptic rendering, as well as spherical-specific applications. suited to simulation of laparoscopic and natural orifice surgeries. In such procedures, the surgeon inserts a rigid III. MECHANICAL DESIGN tool through a small incision (or naturally-ocurring orifice) The basic structure of our device is shown in Figure 1. to gain access to internal structures. To prevent tearing of Kinematically, it can be described as a 3-DOF RRP manip- the entry point, the tool must be constrained to rotate about ulator, where the rotational motions move the tip of an arm and translate through the entry point, which is essentially a along the surface of a sphere, and linear extension of the arm spherical pivot with radial insertion. Although a haptic device changes the radius of that sphere. with non-spherical kinematics could be used to simulate such We use the following definitions of frames and motions: a procedure, we can greatly reduce the physical size of the (refer to Figure 2): simulator and the forces that must be generated by using • The base frame f0g with origin O0 is placed at the spherical kinematics. One such device is a 4-DOF simulator center of rotation of the differential. We align X0 to for vaginal hysterectomies [7]. It uses two grounded motors the user’s right, Y0 forward, and Z0 up. to actuate pitch and yaw and two motors mounted on the • Frame f1g is colocated with frame f0g, and then rotated moving mechanism to actuate roll about the instrument’s axis by an angle φ (pitch) about Y0. and the prismatic, radial DOF via friction rollers. Another • Frame f2g is colocated with frame f1g, and then rotated such simulator is the LaparoscopyVR Surgical Simulator by an angle γ (yaw) about X1. (CAE Healthcare, Montreal,´ Quebec)´ [8], which simulates • Frame f3g is aligned with frame f2g but offset along abdominal laparoscopic surgeries with the same 4 degrees Z2 to coincide with the end-effector. The radial variable of freedom as in [7]. It grounds all 4 motors for reduced is ρ; the distance between the frame origins O0 and O3 inertia and uses a complicated system of cables that route is r = ρ + Re, where Re = 195:5mm. through the entire mechanism to actuate each DOF. • The home position of the device (φ = 0, γ = 0, ρ = 0) We believe that our device improves on these previous is when the arm is vertical and fully retracted. designs in several respects. In the above devices, actuation of the radial DOF was accomplished either by a motor A. Friction Differential attached to moving links [5] [7], thereby hurting inertia We used a friction differential to achieve pitch and yaw, and compactness, via a transmission with high frictional as shown in Figure 4, for a variety of benefits. 2571 • The parallel structure allows for a smaller, stiffer mech- anism than does a serial mechanism. • Both motors are grounded easily, lowering the inertia of the mechanism and increasing compactness. • The center of rotation of the differential is hollow, allowing for actuation cables to be routed through it. • The use of a friction drive results in zero backlash, fewer machined parts, easier assembly, and a more robust mechanism because the wheels slip under excess torque rather than breaking cables or gear teeth as would happen in a cable or gear differential. The driven plate is preloaded against the drive wheels by means of an adjustable rubber spring. This spring sets the normal force on the wheels, and, thence, the friction and torque transfer capacity of the wheels. Once we have determined the wheel material and desired preload, the only way to increase torque transfer capacity is to increase the diameter of the drive wheels, in the case of pitch, and Fig.